In 430BC, at the start of the destructive, long-running war between Athens and Sparta, the great Athenian statesman Pericles made a speech in honour of his city's war-dead. The speech, recorded by the historian Thucydides, is a great and moving account of ancient democratic values. Everyone is equal before the law in our city, says Pericles. We are tolerant, free and open. Finally, he remembers to mention the women of Athens. "The greatest glory of a woman is to be least talked about by men, whether they are praising you or criticising you," he says, quellingly. And that's it.

And yet, there was more to classical womanhood than Pericles's silent and undiscussed matrons. (His own long-term girlfriend, Aspasia, was certainly talked about then and now; famously clever and sophisticated, she was attacked in the comic plays of the time because of her supposed influence over the statesman.) Next week the Cheltenham literature festival is to stage a debate in which novelist Stella Duffy, historian Lucy Hughes-Hallett and broadcaster and writer Bettany Hughes will each champion their own favourite "ancient heroine". I'll be chairing, and the audience will vote on which of these fabulous females is the day's favourite. The identities of the speakers' chosen women – who may be real, or drawn from literature or myth – are not to be revealed until the day. But the classical world gives them plenty of women to choose from. Below are some of my favourites. If sometimes these women seem more harridans or harlots than heroines, we might remember Anne Elliot in Persuasion: "Men have had every advantage of us in telling their own story . . . the pen has been in their hands."

Antigone Mythical heroine of Sophocles's play of the same name, she defies the explicit command of her uncle Creon, king of Thebes, and gives her dead brother, who died a traitor, his proper funeral rites – a crime punishable by death. A standard-bearer for courage in the face of brutish (male) authority.

Athena Surely the best Olympian deity, Athena (also known as Athene) is the goddess of craft, technology, ingenuity, and, crucially, winning. She is Odysseus's protector in the Odyssey, on hand to provide magical disguises or pep-talks.

Artemisia In Herodotus's Histories we see this queen of Halicarnassus (now Bodrum in Turkey) fighting on the Persian side in the war with Greece. Witnessing the battle of Salamis, King Xerxes of Persia was pleased to see the vessel she was commanding ram an enemy ship. "My men have turned into women and my women into men," he remarked. What she'd actually done was ram a friendly ship (all hands lost) to put off the Athenian vessel that was advancing her way. The Athenians assumed she was on their side and backed off.

Boudicca British, of course, but gets on to the list by being known to us through Roman sources. In the early years of Roman rule in Britain her husband, Prastutagus, king of the Iceni in East Anglia, died leaving the Roman emperor, along with his own two daughters, as joint heirs to his lands. But the daughters were raped by Romans and Boudicca was flogged. Boudicca rose up in rebellion and ravaged Colchester, St Albans and burned London to the ground. Not until the Great Fire and the blitz would the city again be visited by such destruction. A poster-girl for anti- imperial resistance, she possessed "more spirit than is usual among women", wrote historian Cassius Dio.

Circe In the Odyssey, Circe turned visiting men into pigs. What more can I say?

Cleopatra She was the 1st century BC pharaoh of Egypt and Rome's favourite exotic temptress. Fighting a civil war against her husband (who was also her brother), she had smuggled herself into the palace where Julius Caesar was staying by having herself rolled up in a carpet. She enlisted him to her cause and became his lover. Later, she famously became embroiled with Mark Antony. Behind the Roman propaganda one can discern a pretty wily politician.

Clodia Metelli The epitome of the chic, sexy, scandalous aristocrat of 1st century BC Rome, Metelli was supposedly the "Lesbia" to whom the love-lorn poems of Catullus are addressed (and if so, a total ball-breaker). In a speech in the lawcourts, Cicero referred disparagingly to her colourfully louche life of affairs, adulteries, beach parties, banquets and drinking sessions. She was widely suspected of having poisoned her first husband. Not necessarily a role model.

Clytemnestra Also not necessarily a role model, since in Aeschylus's play Agamemnon, this mythical character plots her husband's murder when he returns victorious from the sack of Troy. However, she was pushed: he had sacrificed their daughter Iphigenia to the gods to secure a favourable wind across the sea to Troy.

Dido In Virgil's Aeneid, the queen of Carthage, an exile from Tyre after the murder of her husband, was doing very nicely thank you very much, founding a new city in what is now Tunisia. And then Aeneas, an exile from defeated Troy, turned up. The pair fell in love and consummated their passion; but their happiness was cut short when the gods demanded that he leave for Italy. Understandably upset by one of the most brutal dumpings in literature, Dido committed suicide by stabbing herself with his sword. Good use of phallic symbolism, madam.

Gorgo In Herodotus's Histories, Gorgo, a smart Spartan, turns up first as a child, dishing out some good advice to her father during a diplomatic meeting. Later, in the run-up to the Persian wars of the 480s BC, when she is married to Leonidas, later the leader of the fatal 300 at Thermopylae, the Spartans receive a letter – a wax tablet – with nothing written on it. Gorgo has the bright idea of scraping off the wax. Lo, scratched into the wood beneath is a message warning of the coming Persian invasion. She is, therefore, basically the Ruth Evershed (from Spooks) of the ancient world.

Helen The face that launched a thousand ships and all that. And she's Zeus's daughter, and so special. In Homer she is otherworldly, insightful, clever and graceful – an ambiguous figure, of course, because by absconding with the Trojan prince Paris, leaving her Spartan husband Menelaus, she supposedly caused the war. In the Odyssey, she is portrayed as tactful, smart and a good deal brighter than her husband Menelaus.

Hypatia The Alexandrian Hypatia, who died in AD 415 is the first woman philosopher-mathematician known to history. She worked on geometry, astronomy and neoplatonic philosophy and was a popular teacher. She attracted ire for her political connections, and was murdered by fanatical Christians. "Hypatia was torn from her chariot," wrote Gibbon in his Decline and Fall of the Roman Empire, "stripped naked, dragged to the church, and inhumanly butchered by the hands of . . . a troop of savage and merciless fanatics: her flesh was scraped from her bones with sharp oyster-shells, and her quivering limbs were delivered to the flames."

Livia Hard not to think of Siân Phillips's chilling portrayal of her in the classic BBC TV series I, Claudius. This, as in Robert Graves's original novel, draws on the works of the ancient biographer Suetonius, to depict the wife of the emperor Augustus as a monstrous schemer, poisoning every unfortunate who got in the way of her plan to have her own son Tiberius (from her first marriage) installed as Augustus's successor as emperor. She succeeded.

Medea In Euripides's play of the same name, she is the wife of Jason, seeker of the Golden Fleece. When he leaves her for a younger model, she delivers a remarkable speech on the lot of married women, culminating in the memorable line: "I'd rather stand in the battle line three times than give birth once." She does rather blot the feminist copybook by murdering her own children in revenge against their father.

Penelope In the Odyssey, she is the wife of Odysseus. She has traditionally been regarded as a model of fidelity, since she waits for 20 years for him to return home from the Trojan wars, but there is more to her than that. Wily and smart, she is more than a match for the suitors who attempt to claim her in his absence; and she is no pushover, either, when Odysseus finally turns up.

Sappho She is the great woman poet of antiquity. Born on Lesbos in the second half of the 7th century BC, she wrote poems of love and longing, marriage hymns and invocations to the gods. She was hugely admired in antiquity and praised as the "female Homer". She was also imitated – one of her most exquisite poems was translated into Latin by Catullus. Her poems exist in fragments and scraps, but nine volumes of works were said to be in the possession of the great library at Alexandria. Little is known of her life and she has been appropriated as everything from gay icon to model matron.

Tomyris It's oddly little known now how this queen of the Massagetae in central Asia, according to Herodotus, defeated the great king Cyrus of Persia in battle in 530BC. After he had been killed, she plunged his head into a wineskin full of human blood – since he had successfully tricked her troops and captured her son by getting them drunk.

• Charlotte Higgins is the author of It's All Greek To Me, published by Short Books, £12.99

• This article was amended on 8 October 2010. The original referred to Jason as the king of Athens. This has been corrected.